Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.

** Well-ordering theorem: Every set can be well-ordered.

Every information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.

Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.

* Every regular language is context-free because it can be described by a context-free grammar.

Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.

Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as

Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.

Every entire function can be represented as a power series that converges uniformly on compact sets.

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:

Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

Every hyperbola is congruent to the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it can be rotated so that it opens in the desired direction and can be translated ( rigidly moved in the plane ) so that it is centered at the origin.

Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.

Every species can be given a unique ( and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.

Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

Every morpheme can be classified as either free or bound.

Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication.

Every document window is an object with which the user can work.

Every adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in a lifetime.

Every ordered field can be embedded into the surreal numbers.

* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.

* Every preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.

Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.

Every yacht should carry at least two anchors – the main or bower anchor and a second lighter kedge anchor.

* Every collecting institution must develop an emergency plan to protect its collections and train staff to carry it out.

Every fifth person in Germany is thought to carry Salmonella.

Every class can carry a primary and secondary weapon, which are organized into " kits ".

Every vessel taking part in Green was to carry anti-aircraft weaponry indicating that the planners expected the Royal Air Force ( RAF ) to intercept them, although air cover from the Luftwaffe's West of France Air Command was to be provided as part of Sea Lion.

In Spain, a wallet was a case for smoking paraphernalia: " Every man would carry a small sheaf of white paper in addition to a small leather wallet which would contain a flint and steel along with a small quantity of so-called yesca, being a dried vegetable fibre which a spark would instantly ignite.

Every year chanichim ( members ) travel to Israel for a year on Shnat Hachshara le ' Aliyah Ve ' Hadracha, commonly referred to as Shnat, where they go on an extensive experiential and educational process and actively carry out movement aims and discuss group issues.

Every spacecraft can only carry a limited amount of upgrades, as they all have a maximum upgrade capacity.

Every man who could carry arms down to twelve year-olds, and every horse from two years of age and older.

Every dance must have at least one woman with shakers, who falls into step immediately behind the song leader, to carry the rhythm.

* Revised Code of Washington 9. 12. 010: " Every person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state.

Every year 12 new students are accepted to the school.

Pirate luminaries such as William Kidd, Henry Every, John Bowen, and Thomas Tew made Antongil Bay and Nosy Boraha ( St. Mary ’ s Island ) ( a small island 12 miles off the north-east coast of Madagascar ) their bases of operations.

Every year, it invites entries of unpublished African-inspired stories written for an audience of 8 to 11-year-olds ( Category A ) or 12 to 15-year-olds ( Category B ) and by writers aged 18 or below ( the Rising Writer Prize ).

Every day about 37, 000 people come to Zug to work, 12, 000 of whom are from the canton of Lucerne.

Every Friday morning ( 10. 00 – 12. 30 a. m .) the Waagplein is the backdrop for this traditional cheesemarket.

Every male Weyrbrat has the right to become a Candidate and stand for Impression at age 12.

Every 12, 500 soldiers were counted as one jun.

He went on to birdie the last hole, sinking a 12 foot birdie putt for a two stroke victory over Matt Every and John Huh.

* LBJ-030 Bright Eyes-Every Day and Every Night EP CD / 12 "

Every year, on April 12, the Historic Halifax State Historic Site celebrates Halifax Day.

Every specialty offers 12 different spells or abilities to choose from.

" Lift Every Voice and Sing " was publicly performed first as a poem as part of a celebration of Lincoln's Birthday on February 12, 1900 by 500 school children at the segregated Stanton School.

As stated by the WHO in its 2005 World Health Report " Make Every Mother and Child Count ", the major causes of maternal deaths are: severe bleeding / hemorrhage ( 25 %), infections ( 13 %), unsafe abortions ( 13 %), eclampsia ( 12 %), obstructed labour ( 8 %), other direct causes ( 8 %), and indirect causes ( 20 %).

Every 20 Tactics allow the player to control 1 more unit in battle, from the basic 6 units up to 12 units with 120 Tactics.

Every 12 points, the player is awarded a new promotion.

Every digit in the machine had one parity bit, for error checking, meaning every word occupied 60 bits ( 48 bits for data with 12 bits for parity check ).

# "... And in Every Home " ( Rehearsal ) – 3: 12

After it, the duo charted at number 5 with " My Heart Is Lost to You " and number 12 with a cover of Kim Richey's " Every River ", featuring a backing vocal from Richey.

Their third album Every Man for Himself was released in May 2006 and debuted at No. 12 on the Billboard chart.

* " Every Time Mix " and " Tarzan Mix " on Remixes 12 " ( 1998 )

Every day it caters for approximately 12. 000 students.

The Great Seal is protected under the Security of Information Act, Section 5 ( 2 )( e ) stating: " Every person who, without lawful authority or excuse, manufactures or sells, or has in his possession for sale, any die, seal or scribble referred to in subsection ( 1 ) is guilty of an indictable offence and liable to imprisonment for a term of not more than 14 years or by summary conviction and liable to imprisonment for a term of not more than 12 months or to a fine of not more than $ 2, 000.

Every year, 12 artists are awarded Kuitka scholarships, which allows them to meet with modern artist Guillermo Kuitca once a week to discuss their artwork.